This game is the definitive sandbox game. I haven't been excited to get out of work to go home and play a video game in a long tyme. But this game did it. Basically the premise is this:

You start out in a huge world with nothing. It is morning. You need to acquire some building materials during the day in order to build a crude shelter to stay in during the night. Since you start with nothing, you must gather wood by punching down a tree. Seriously. When night falls, the monsters come: zombies, skeletons, giant spiders, and creepers. If you have built a good enough shelter, you can spend the night crafting tools, weapons, armor, sturdier building materials, and many other things. If you did not, you will either spend the night running in terror or else die. When morning arrives, the undead monsters will die, but the others will remain, waiting for you right outside your shelter. After fighting your way out, you are free to explore again, gathering more resources and entering caves. The caves often hold valuable ores and sometimes even treasure, but the monsters are safe from the sunlight in the caves and will attack you. Eventually, you can construct larger and safer shelters, but it will always be dangerous to wander too far from home. Getting lost is very easy in the enormous world. The cycle of day and night continues and you can eventually build fantastic structures.

If that text wall got you pissed, then these two links will sum the game up perfectly: